locus Z ( Σ ) ∶ = V ( B Σ ) in the aﬃne space A d ∶ = Spec ( S ) is the irrelevant locus.\n\nProposition 2.3 (Theorem 5.1.11 [5]) . The toric variety P d Σ is a categorical quotient A d ∖ Z ( Σ ) by the group Hom ( Cl ( Σ ) , C ∗ ) and the group action is induced by the Cl ( Σ ) - grading of S .\n\nNow we give a brief introduction to complex orbifolds and we mention the needed theorems for the next section. Namely: de Rham theorem and Dolbeault theorem for complex orbifolds.\n\nDeﬁnition 2.4. A complex orbifold of complex dimension d is a singular complex space whose singularities are locally isomorphic to quotient singularities C d / G , for ﬁnite sub- groups G ⊂ Gl ( d, C ) .\n\nDeﬁnition 2.5. A diﬀerential form on a complex orbifold